Further Reading: Chapter 25

Time Series Analysis and Forecasting

Foundational Texts

1. Forecasting: Principles and Practice --- Rob J. Hyndman and George Athanasopoulos (3rd edition, 2021) The single best introduction to time series forecasting. Hyndman (creator of the forecast package in R and co-creator of many forecasting methods) writes with extraordinary clarity. The book covers decomposition, exponential smoothing, ARIMA, dynamic regression, and hierarchical forecasting, all with real data examples. The third edition is freely available online at otexts.com/fpp3. Even though the code examples are in R, the conceptual material is language-agnostic and essential. If you read one book on forecasting, read this one.

2. Time Series Analysis and Its Applications --- Robert H. Shumway and David S. Stoffer (4th edition, 2017) The standard graduate-level textbook for time series. More mathematically rigorous than Hyndman, with thorough coverage of ARIMA theory, spectral analysis, state space models, and multivariate time series. The "with R Examples" subtitle understates the theory depth. Chapters 3-4 (ARIMA models and ARIMA estimation) are the definitive treatment. Free companion materials at the authors' website.

3. Introduction to Time Series and Forecasting --- Peter J. Brockwell and Richard A. Davis (3rd edition, 2016) A mid-level text that bridges Hyndman's practitioner focus and Shumway/Stoffer's mathematical rigor. Strong coverage of stationarity conditions, the Wold decomposition theorem, and spectral methods. Chapter 5 (modeling and forecasting with ARMA processes) is particularly well-written.

ARIMA and Classical Methods

4. "Time Series Analysis: Forecasting and Control" --- George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung (5th edition, 2015) The original Box-Jenkins methodology for ARIMA modeling: identify (using ACF/PACF), estimate, diagnose, forecast. This is the book that defined the field. Dense and mathematical, but the three-stage iterative procedure (identification, estimation, diagnostic checking) remains the gold standard for rigorous time series analysis. The 5th edition adds Ljung as co-author and includes updated computational examples.

5. Applied Econometric Time Series --- Walter Enders (4th edition, 2014) The standard reference for unit root testing (ADF test, KPSS test, Phillips-Perron test) and cointegration. Chapter 4 covers the ADF test in more depth than any other source at the applied level, including the subtleties of choosing lag length and handling structural breaks. Essential for anyone who needs to understand stationarity testing beyond "run the test, check the p-value."

Prophet

6. "Forecasting at Scale" --- Sean J. Taylor and Benjamin Letham (2018) The original Prophet paper, published in The American Statistician. Describes the decomposable time series model (trend + seasonality + holidays) and the practical design decisions that make Prophet work for "analysts who are not time series experts." The paper is refreshingly honest about the tradeoffs: Prophet sacrifices the theoretical rigor of ARIMA for practical robustness and ease of use. Available at peerj.com/preprints/3190.

7. Prophet Official Documentation --- facebook.github.io/prophet The documentation includes quickstart guides, API reference, and detailed explanations of each component (trend with changepoints, Fourier seasonality, holiday effects). The "Diagnostics" section covers Prophet's built-in cross-validation, which uses the walk-forward methodology described in this chapter. The "Saturating Forecasts" page explains logistic growth trends for metrics with natural caps (e.g., market penetration).

Walk-Forward Validation and Evaluation

8. "On the Use of Cross-Validation for Time Series Predictor Evaluation" --- Christoph Bergmeir and Jose M. Benitez (2012) A seminal paper examining when standard cross-validation can (and cannot) be used for time series. The key finding: for purely autoregressive models on stationary data, standard CV can work. But for most practical forecasting problems (non-stationary, seasonal, with exogenous variables), walk-forward validation is safer. Published in Information Sciences, Vol. 191.

9. "Evaluating Time Series Forecasting Models: An Empirical Study on Performance Estimation Methods" --- Vitor Cerqueira, Luis Torgo, and Igor Mozetic (2020) A comprehensive comparison of evaluation strategies for time series: hold-out, repeated hold-out, rolling-origin (walk-forward), blocked cross-validation, and hv-blocked CV. The paper provides concrete recommendations for which evaluation method to use based on dataset size, model type, and forecast horizon. Published in Machine Learning, Vol. 109.

Practical Guides

10. Python for Data Analysis --- Wes McKinney (3rd edition, 2022) Chapter 11 covers time series in pandas: datetime indexing, resampling, time zone handling, period arithmetic, and rolling windows. This is the reference for the data manipulation side of time series --- getting your dates right, resampling from daily to monthly, aligning series with different frequencies. McKinney is the creator of pandas, and this is the authoritative guide.

11. statsmodels Time Series Documentation The statsmodels documentation for tsa (time series analysis) covers ARIMA, SARIMAX, seasonal decomposition, ACF/PACF, the Durbin-Watson test, and much more. The "Statespace Models" section is particularly comprehensive, with worked examples of structural time series models. Available at statsmodels.org/stable/tsa.html.

12. pmdarima (auto_arima) Documentation The pmdarima library wraps statsmodels with an automated ARIMA selection procedure inspired by R's auto.arima. The documentation explains the stepwise search algorithm, seasonal vs. non-seasonal models, and the interaction between AIC selection and parameter constraints. Available at alkaline-ml.com/pmdarima.

Machine Learning Approaches to Time Series

13. "Machine Learning Strategies for Time Series Forecasting" --- Gianluca Bontempi, Souhaib Ben Taieb, and Yann-Ael Le Borgne (2013) A survey paper that covers the ML approach to time series: feature engineering (lags, rolling statistics, calendar features), the distinction between recursive and direct multi-step forecasting, and why cross-validation requires temporal modifications. Published in the Lecture Notes in Business Information Processing series.

14. "Do We Really Need Deep Learning Models for Time Series Forecasting?" --- Shun Zeng et al. (2023) A provocative paper demonstrating that simple linear models with proper feature engineering can match or beat deep learning models (LSTM, Transformer) on many forecasting benchmarks. The implication: the feature engineering and evaluation methodology matter more than the model architecture. An important counterweight to the hype around deep learning for time series.

Deep Learning for Time Series (Preview for Chapter 36)

15. "Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting" --- Bryan Lim, Sercan Arik, Nicolas Loeff, and Tomas Pfister (2021) The paper that introduced the Temporal Fusion Transformer (TFT), which combines variable selection networks, gated residual networks, and multi-head attention for time series. TFT provides both accurate forecasts and interpretable attention-based explanations. Published in International Journal of Forecasting, Vol. 37.

16. "N-BEATS: Neural Basis Expansion Analysis for Interpretable Time Series Forecasting" --- Boris N. Oreshkin et al. (2020) A deep learning architecture for univariate time series that achieves state-of-the-art results through a stack of fully connected networks with basis expansion. Notable for being interpretable (trend and seasonality stacks) and beating statistical methods on the M4 forecasting competition. Published in ICLR 2020.

17. "Are Transformers Effective for Time Series Forecasting?" --- Ailing Zeng et al. (2023) A critical paper showing that a simple linear model can outperform Transformer-based time series models on many benchmarks. The authors argue that the permutation-invariant nature of self-attention may not be well-suited for temporal data, where ordering is fundamental. Published in AAAI 2023. Essential reading before investing in Transformer-based forecasting.

Domain-Specific Applications

18. "Machine Learning for Predictive Maintenance of Wind Turbines" --- Various authors (survey papers) Multiple survey papers cover time series analysis for wind turbine predictive maintenance, including vibration analysis, SCADA data monitoring, and remaining useful life estimation. Search Google Scholar for "predictive maintenance wind turbine time series" for the most recent surveys. The European Wind Energy Association (EWEA) conference proceedings are a rich source.

19. "Predicting Customer Churn: A Systematic Literature Review" --- Amin, A. et al. (2023) A comprehensive review of churn prediction methods, including time series approaches for modeling churn rate dynamics over time. The paper distinguishes between cross-sectional churn prediction (who will churn?) and temporal churn prediction (when will they churn? what will the churn rate be?). Published in Expert Systems with Applications.

Video Resources

20. Ritvikmath --- "Time Series" playlist (YouTube) A well-paced video series covering stationarity, ACF/PACF, ARIMA, SARIMA, and Prophet with Python implementations. Each video is 10-20 minutes and balances intuition with code. The video on "Why Stationarity Matters" is one of the clearest explanations available.

21. Rob Hyndman --- "Forecasting Best Practices" (various conference talks) Multiple recorded talks by the author of "Forecasting: Principles and Practice," available on YouTube. Hyndman's talks on forecast evaluation, forecast reconciliation, and the M4 forecasting competition are particularly valuable. His style is accessible and his opinions are backed by decades of research.

How to Use This List

If you read nothing else, read Hyndman and Athanasopoulos (item 1). It is free, comprehensive, and beautifully written. Pair it with the statsmodels documentation (item 11) for Python implementation.

If you need to understand ARIMA deeply, read Box et al. (item 4) for theory and pmdarima docs (item 12) for practice.

If you are using Prophet, read the Taylor and Letham paper (item 6) to understand what Prophet does under the hood, then the official documentation (item 7) for practical tuning.

If you are considering deep learning for time series, read Zeng et al. (item 14) first --- you may not need it. If you do, start with TFT (item 15).

If you care about getting the evaluation right (and you should), read Cerqueira et al. (item 9) for a rigorous comparison of temporal evaluation strategies.

This reading list supports Chapter 25: Time Series Analysis and Forecasting. Return to the chapter to review concepts before diving in.